WHILE WORKING AN INFLT EQUIP MALFUNCTION; FLT CREW MAY HAVE MISSED AN ALT CLRNC AND OVERSHOT ASSIGNED ALT; RESULTING IN TCAS RA.

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DURING A PART 91 REPOSITION FLT; ON LEVELOFF WE RECEIVED A FLAPS FAIL CAUTION MESSAGE. AT THE SAME TIME WE WERE CLRED TO 17000 FT. BEFORE REACHING THE FIX; WE WERE GIVEN DIRECT TO ANOTHER FIX DOWN TO 11000 FT. AT THE SAME TIME THE PNF WAS RUNNING QRH ITEMS FOR A FLAPS FAIL CAUTION MESSAGE; AND IN THE PROCESS OF CONTACTING COMPANY ON COM 2 REGARDING A FLAPS FAIL CAUTION MESSAGE. ATC WAS ALSO ADVISED OF THE FLAPS FAIL; INFORMED THAT OUR MAX SPEED WAS LIMITED TO 250 AND THAT WE MIGHT NEED DELAY VECTORS OR A HOLD IN ORDER TO SORT OUT THE CAUTION MESSAGE WITH COMPANY. (DURING THIS WHOLE TIME WE ALSO RECEIVED SEVERAL HDOFS.) WE THEN REQUESTED AND RECEIVED A DELAY VECTOR; WHILE ON THE VECTOR WE CONTINUED THE DESCENT DOWN TO 11000 FT. AT 12000 FT WE RECEIVED AN RA ON THE TCAS AND INITIATED A CLB TO 13000 FT. DURING THE CLB ATC ALSO GAVE US A CLB TO 13000 FT. ATC ALSO STATED THAT WE WERE NOT CLRED BELOW 13000 FT. WE BELIEVE THAT WE WERE STILL CLRED DOWN TO 11000 FT. DURING THIS TIME (BETWEEN 13000 FT AND 11000 FT) COMPANY ADVISED US THERE WAS NO WAY TO FIX THE PROB IN THE AIR. SO WE DECLARED AN EMER; ADVISED ATC THAT OUR FLAPS WERE STUCK IN A POSITION THAT WAS INDICATING UP; AND OUR LNDG SPEED WOULD BE CONSIDERABLY HIGHER. WE REQUESTED THE LONGEST RWY AND TO HAVE EMER EQUIP STANDING BY. THE LNDG WAS UNEVENTFUL; NO INJURIES; OR DAMAGE TO THE ACFT. WE HAD THE EMER VEHICLES VERIFY THAT OUR TIRES AND BRAKES WERE NOT ON FIRE AND TAXIED TO THE GATE. AT THE GATE MAINT WAS BROUGHT OUT TO THE ACFT. I BELIEVE THE CAUSE OF THE RA WAS EITHER US MISSING A RADIO CALL TO STOP DESCENT AT 13000 FT; OR THE CTLR ISSUING THE VECTORS NOT KNOWING THAT WE WERE CLRED DOWN TO 11000 FT BY THE PREVIOUS CTLR. IN EITHER INSTANCE; THE ONLY CORRECTION THAT I KNOW OF WOULD BE BETTER COMMUNICATION BETWEEN ACFT AND ATC.